US-Russian relations are under the spotlight ahead of Secretary of State Rex Tillerson's visit to Russia next week.

Questions have been raised over the future of US-Russian ties after Washington launched a barrage of tomahawk missiles against an airbase in Syria, where Russia's military is on the ground propping up its ally, President Bashar al-Assad.

US Secretary of State Rex Tillerson will next week make the first visit to Russia by a Trump administration official, just days after the US strike on Shayrat airfield in Homs province - described as a response to a suspected chemical attack in the Idlib province, blamed by many on Assad.

The attack, as well as multiple Russia-related investigations in the US, will follow Tillerson's trip, which was designed to test the Trump administration's hopes for closer ties to its former Cold War foe.

The Pentagon said limited warning had been given through the normal de-confliction channel used by both sides, but Tillerson said that no approval was sought from Moscow.

Matthew Schmidt, a Russia expert and assistant professor of national security at the University of New Haven, sad that Russia is likely to take several steps to increase the pressure on the US if it keeps bombing Assad.

If Washington was to deploy manned aircraft, Schmidt said, Russia could take steps such as exposing them on radar "to kind of say, 'if we wanted to shoot you down, we could shoot you down', and Putin will use this to sort of increase the pressure and the threat on the US".

Lawrence Korb, a former US secretary of defence and senior fellow at the Center for American Progress, said he thought that Russia would privately be upset with Assad.

"I think that they did not want to give the United States an excuse to go after Assad," said Korb.

"The Russians are going to say 'we don't want this to escalate anymore'," said Korb. "So I think it may lead to a temporary ceasefire while the parties talk and divide up the country, and then talk about Assad [possibly] stepping down in 2020."

Tillerson, speaking just after the strikes were announced, said Russia had "failed in its responsibility" to deliver on a 2013 deal it helped broker to destroy Syria's chemical weapons arsenal.

"So either Russia has been complicit, or Russia has been simply incompetent on its ability to deliver," Tillerson said.

Despite Trump's much-hyped campaign talk about a Russia reset, there's no appetite for that from either political party in the US, analysts say.

Even minor concessions to Russia would trigger immediate accusations from Trump's opponents that the president - who has praised Putin generously and repeatedly - is beholden to the Russian leader.

The US State Department said Tillerson had spoken by phone to Russian Foreign Minister Sergey Lavrov after Tuesday's suspected chemical attack in Khan Sheikhoun, in northwest Syria.

Russia has maintained that Syrian air strikes hit a depot where anti-Assad rebels were building chemical weapons, a claim the US has vigorously disputed.

Tillerson's close ties to Russia - Putin once gave him the "Order of Friendship" award - drew serious concerns during his confirmation hearings, but he has since emerged as one of the Trump administration's more sober voices about Moscow's behaviour.

Senior State Department officials described Tillerson's visit as an "exploratory trip" aimed at determining any potential for cooperation, adding that no decisions to increase cooperation had been made.

Tillerson may or may not meet with pro-democracy activists in Russia, as members of congress have urged, the officials said.

US relations with Russia sharply deteriorated in 2014, following the annexation of Crimea. The Obama administration and Western countries slapped Moscow with severe economic sanctions that Trump has so far vowed to keep in place.

Still, Putin's government has been optimistic about Trump's presidency.

Until Tuesday's suspected chemical attack in Syria, Trump and his deputies said their top focus in Syria was fighting ISIL - not ousting Assad - a position that aligned with Putin's own publicly stated goal.

Schmidt said that Russia is likely to veto any action in response to the alleged chemical attacks at the UN Security Council on the grounds of Syria's sovereignty.

He added that without massive numbers of troops on the ground, missile strikes by the US are unlikely to change the trajectory of the conflict, which has seen Assad make significant recent battlefield gains on the battlefield with Russian and Iranian support.

"Putin will look at Trump and he will say 'Trump is weak'," Schmidt argued.

"[That Trump] bombed out of an emotional response, that he is unconnected to a thought-out policy. Trump is not a chess player - and Putin plays long-term, slow, three-dimensional chess. So he sees Trump as someone he can play, not as someone he can play with, because Trump's just not on his level of strategic games."